PoreML: A Data-Driven Framework for Learning Multiphase Flow in Porous Media

Detailed Research Summary of PoreML: A Data-Driven Framework for Learning Multiphase Flow in Porous Media

PoreML is an open-source, physics-grounded framework designed to unify data generation, model training, and evaluation for learning multiphase flow within porous media. Its primary goal is to empower the research community to develop reliable predictive models for this complex physical system. The framework is structured around three core components: a validated data generation engine, an extensive dataset, and an integrated learning benchmark.

Core Components of PoreML

1. Data Generation Engine (Solver):

The foundation of PoreML is a modern, GPU-native Lattice Boltzmann Method (LBM) solver. This solver is rigorously validated against both analytical solutions and published experimental data across an eight-case suite. It utilizes the Color-Gradient Lattice Boltzmann Method (CG-LBM) to model the physics, ensuring that component distribution functions yield hydrodynamic limits consistent with Navier–Stokes equations, thereby accurately capturing fluid motion and interface evolution on a common lattice.

The solver is designed to generate reproducible data by pairing each wetting boundary condition with the surface-tension formulation from its original source publication. Key boundary conditions include:

• Piston Inlet: Simulating non-wetting phase injection at a precise volumetric rate, driving displacement experiments where capillary number (Ca) is directly controlled.

• Pressure Inlet/Outlet: Using per-color Zou–He pressure boundaries to fix reservoir plane densities, allowing control over purely capillary-driven imbibition or pressure-controlled drainage by varying the inlet-outlet density difference (P).

• Outflow: A density-rescaled copy of the penultimate plane for free wetting phase exit.

Crucially, the solver handles complex geometries by computing wall normals from a solid mask rather than relying on known analytical solutions for curved surfaces (e.g., in sphere packs or rock crops), ensuring fidelity across the dataset's varied geometries.

2. The PoreML Dataset:

PoreML boasts an open and extensive dataset, described as the first and largest to provide time-resolved, full 3D fluid distributions for multiphase flow in porous media. This dataset is substantial, containing 560 simulation runs and 158,546 stored time steps across four distinct application-driven scenarios.

The data is uniquely comprehensive, spanning:

• Geometries: A pairing of generated structures with real geometries obtained from microcomputed tomography (mu CT) scans, covering multiple domain sizes and wettabilities.

• Scenarios: Four application-driven scenarios.

• Parameters: A grid of wettabilities and viscosity ratios.

The data is meticulously organized and adheres strictly to FAIR principles:

• Findable: Data and geometry collections reside at public Hugging Face addresses with descriptive metadata.

• Accessible: Data can be downloaded without registration via command-line utilities or framework tools.

• Interoperable: Trajectories are stored as HDF5 files with Zstandard compression, paired with an XDMF index for ParaView visualization; geometries are stored as NumPy arrays.

• Reusable: The solver, framework, and dataset are released under permissive licenses (MIT/CC 4.0). Every run is traceable via recorded solver settings, software environment, and input geometry hash.

3. Unified Learning Framework:

The framework provides a standardized environment for machine learning research on multiphase flow in porous media. It facilitates:

• One-Step Prediction: Training models to predict the next time step based on the current state.

• Autoregressive Rollouts: Evaluating models over extended sequences (e.g., 64 steps) to assess long-term predictive capability.

The evaluation protocols are domain-specific, assessing not only predictive accuracy but also physical consistency. PoreML employs advanced metrics to quantify this consistency:

• Minkowski Functionals: Used as state variables of two-fluid flow in porous media, established by prior literature (Armstrong et al., 2016; McClure et al., 2018).

• Mean Curvature: Tied to the Young–Laplace equation, which governs capillary pressure (Blunt, 2017).

• Euler Characteristic (chi): Quantifies topological fidelity by measuring connected components (beta 0), tunnels (beta 1), and enclosed bubbles (beta 2). The formula is chi = beta 0 - beta 1 + beta 2.

Key Contributions and Findings

PoreML's contributions are threefold:

(1) Open-Source Solver: A GPU-sharded LBM solver validated on an eight-case suite, enabling community data generation for novel geometries and conditions.

(2) Comprehensive Dataset: The first and largest dataset providing time-resolved, full 3D fluid distributions across diverse physical conditions and geometries.

(3) Integrated Learning Benchmark: A standardized evaluation protocol assessing five benchmark architectures using metrics covering field accuracy, geometry fidelity, and topology.

Insights from Evaluation:

The framework reveals critical failure modes in current approaches. Specifically, the analysis of rollout failures (Appendix I) shows that voxel-level errors can close loops and fill films—phenomena that traditional field loss metrics often fail to penalize adequately. PoreML addresses this by introducing topological accounting:

• Topological Accounting: The Euler characteristic decomposition explicitly tracks specks (islands/bubbles, adding +1), tunnels (subtracting-1), and bubbles, providing a metric that captures connectivity beyond simple voxel-level errors.

• Physical Consistency Check: While low field error does not guarantee correct connectivity (topology), the framework demonstrates encouraging transfer capabilities in Geo-Shift tests (transfer to mu CT scans) and Scale-Up tests (doubling spatial dimensions). However, the analysis highlights that preserving physically meaningful phase topology over long rollouts remains a key area for future research.

In summary, PoreML provides a shared, robust foundation—a solver for generating physically accurate data, a massive dataset spanning diverse physical regimes and geometries, and an integrated benchmark utilizing sophisticated metrics (Minkowski functionals and Euler characteristic) to rigorously test the predictive capabilities of machine learning models in multiphase flow.

1. Bold header: Improved topological fidelity during autoregressive rollouts. The framework assesses whether a 64-step rollout keeps the interface geometry and topology that govern capillary dynamics, which is crucial because low field error does not guarantee the right connectivity.

2. Bold header: Physics-grounded metric refinement for topological accuracy. Instead of relying solely on MAE, the system should prioritize metrics like the MAE of the Euler characteristic per unit volume, as this keeps it comparable across domain sizes and is explicitly used to quantify whether a prediction engulfs a fiber or bridges two regions with a voxel-thin strand closes a loop and lowers the Euler characteristic by one.

3. Bold header: Specialized error mitigation for GDL geometries. Since GDL geometries are noted as favoring tunnels, the system should be trained with representations that can distinguish between specks (discretization noise) and tunnels (handles of the invading phase), which are quantified by the Euler characteristic decomposition.

4. Bold header: Geometry-aware conditioning for transferability. The learning framework must explicitly condition its predictions on geometry, as specified by the unified learning framework, enabling effective transfer between synthetic structures and real microCT-derived materials (Geo-Shift transfers models from generated structures to real rock and carbon-paper geometries).

Multiphase flow in porous microstructures is central to CO 2 storage, fuel-cell operation, and flip-chip packaging. Predicting these flows remains challenging because wettability and complex pore geometry govern the nonlinear evolution of fluid interfaces. Machine learning holds substantial promise for advancing the field, but progress is constrained by scarce time-resolved 3D datasets and a lack of a unified workflow for training and evaluating models. To fill this critical gap, we introduce PoreML, an open-source framework unifying data generation, model training, and evaluation grounded in pore-scale physics. The framework comprises three core components. (a) A modern GPU-native lattice Boltzmann solver, validated against analytical solutions and published experiments, enables reproducible data generation. (b) A 3.3 TB dataset contains 560 simulation runs and 158,546 stored time steps across four application-driven scenarios. These trajectories span synthetic structures and geometries derived from micro-CT scans of real materials, covering diverse wetting conditions and viscosity ratios. (c) A unified learning framework evaluates one-step prediction and autoregressive rollouts. Its domain-specific evaluation protocols assess predictive accuracy and physical consistency. We evaluate five models of diverse architecture under these protocols. Two complementary challenges assess transfer to larger domains and from synthetic to micro-CT-derived structures. PoreML provides a shared foundation for machine-learning research on multiphase flow in porous media, with the aim of empowering the community to develop reliable predictive models and advance the field.